2012/06/14 by Miguel Angel Alejo, Claudio Muñoz · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.AP #math.MP
paper · pdf · doi:10.1007/s00220-013-1792-0
24 pp., submitted
arxiv created 2012/06/14 · arxiv updated 2015/06/05
Breather solutions of the modified Korteweg-de Vries equation are shown to be globally stable in a natural H2 topology. Our proof introduces a new Lyapunov functional, at the H2 level, which allows to describe the dynamics of small perturbations, including oscillations induced by the periodicity of the solution, as well as a direct control of the corresponding instability modes. In particular, degenerate directions are controlled using low-regularity conservation laws.